Wu et al. reply

replying to C. Tomasetti et al. Nature 548, 10.1038/nature23302 (2017)

In the accompanying Comment¹, Tomasetti et al. consider the tumorigenic effects of both ‘random mutations’ (intrinsic) arising during DNA replication, as well as mutations that occur owing to environmental (extrinsic) and inherited factors, driving the discussion into the domain of estimating the contributions of extrinsic factors alongside intrinsic/unmodifiable factors. Originally, Tomasetti and Vogelstein estimated the contribution of intrinsic factors as 64% on the basis of the correlation between stem-cell division and lifetime cancer risk². However, our thought experiment (figures 1 and 2 in our study³) showed that this correlation does not distinguish the effects of extrinsic versus intrinsic mutagens acting at the level of cell division. We further provided four distinct approaches to estimate the contribution of extrinsic factors, and they all converge on an estimate of 70–90% (that is, a contribution of intrinsic factors at 10–30%).

Tomasetti et al. state that the seven cancer types we used to define the ‘intrinsic’ risk line have ‘zero intrinsic risk’. However, in our study, we stated that the ‘intrinsic’ risk lines themselves represent an upper estimate of intrinsic risk, allowing that these cancers are likely to have extrinsic components. Tomasetti et al. further state that in our robustness analyses, we did not consider noise of stem-cell divisions for these cancers. However, we added noise estimates to all cancer types, including those seven cancers. Indeed, we also observed that the same seven cancers were also the same as those defining the ‘intrinsic’ risk line in most simulation cases³.

Tomasetti et al. argue that if the seven cancer types at the top of our figure 3a were used to define an upper boundary line and assume an extrinsic risk of 90% for the upper boundary line, an averaged 80% total risk could be attributed to intrinsic factors. However, as per our analyses, that assumption would lead to more than half of the cancer types, including those known to have substantial extrinsic risks, to show negative extrinsic risks. This implies that either the regression for the upper boundary line or the assumption of extrinsic risk of 90% for the upper boundary line is unfounded. If we adopt the approach of Tomasetti et al. and use the upper boundary line but associate 99.9% extrinsic risk (consisting of cancers known to be nearly exclusively induced by known extrinsic factors), the majority of cancer types still remain above the 90% extrinsic risk line, in agreement with our conclusions.

Tomasetti et al. performed simulations to evaluate the effect of noise and conclude that our lower-boundary approach overestimated the extrinsic risk. However, some of their simulation settings could lead to erroneous conclusions. In particular, in their simulation, they assume that the extrinsic risks of all cancers is 10%; however, this contradicts their simultaneous use of a regression slope of 0.52 between log₁₀(cancer risk) and log₁₀(stem-cell division), because they derived the slope of 0.52 from their previous data, in which many cancers are already known to have substantial extrinsic risks (more than 10%). Indeed, as shown in figure 3a of our study³, the estimated slope for cancers with relatively more intrinsic risk is 0.27 (the intrinsic risk line), that is, considerably different to 0.52 on the log₁₀ scale. Thus, we feel that owing to potentially erroneous assumptions contradictory to the observed data, their simulation cannot be used to dispute our method.

In their Comment¹, Tomasetti et al. mention that we assumed that there is a linear relationship between cancer incidence and stem-cell divisions among cancer types with the same extrinsic risk. However, we did not make that assumption, and the key assumption that we did make was direct and biologically based: cancers with the same number of stem-cell divisions should share the same intrinsic cancer risk if the relationship between total stem-cell division and cancer risk is causal. Therefore, for any two cancers with the same total stem-cell division, the one with the higher incidence of cancer must represent the contribution of extrinsic risk.

Tomasetti et al. raised further concerns regarding the other approaches we used. Although we agree with some of these points, such as incorporating clonal dynamics into future modelling for more accurate estimates, we cannot agree that ours are faulty because of overly liberal assumptions. The clonal expansion issue was partly addressed in our model that assumes every tissue cell to be a stem cell (figure 4b in our study³), which can be viewed as clonal expansion to the tissue size at the very early stage. Under this conservative assumption, the theoretical intrinsic risks are still found to be quite low. Estimation of extrinsic risks from mutational signatures is also conservative as extrinsic factors may cause cancers through many avenues. We realize that each approach has its own limitations, which led us to employ four independent approaches, each of which showed high concordance.

Author S. Powers was not available to work on this Reply.